Using a global 3D, fully self-consistent, multi-fluid hydrodynamic model, we simulate the escaping upper atmosphere of the warm Neptune GJ436b, driven by the stellar XUV radiation impact and gravitational forces and interacting with the stellar wind. Under the typical parameters of XUV flux and stellar wind plasma expected for GJ436, we calculate in-transit absorption in Lyα and find that it is produced mostly by Energetic Neutral Atoms outside of the planetary Roche lobe, due to the resonant thermal line broadening. At the same time, the influence of radiation pressure has been shown to be insignificant. The modelled absorption is in good agreement with the observations and reveals such features as strong asymmetry between blue and red wings of the absorbed Lyα line profile, deep transit depth in the high velocity blue part of the line reaching more than 70%, and the timing of early ingress. On the other hand, the model produces significantly deeper and longer egress than in observations, indicating that there might be other processes and factors, still not accounted, that affect the interaction between the planetary escaping material and the stellar wind. At the same time, it is possible that the observational data, collected in different measurement campaigns, are affected by strong variations of the stellar wind parameters between the visits, and therefore, they cannot be reproduced altogether with the single set of model parameters.Keywords: hydrodynamicsplasmasplanets and satellites: individual: exoplanetsplanets and satellites: physical evolutionplanets and satellites: atmosphereplanet-star interactions 2004, García Muñoz 2007, Koskinen et al. 2007) clarified the basic physics of the escaping upper atmosphere in the form of planetary wind (further PW), which includes the XUV heating, hydrogen plasma photo-chemistry, radiation cooling, gravitational and thermal pressure forces. They helped to explain some of the in-transit spectral observations by the presence of an expanded partially ionized upper atmospheres, which fill the Roche lobes of hot giant exoplanets, such as HD209458b and HD189733b (Ben-Jaffel 2007, Ben-Jaffel & Sona Hosseini 2010, Koskinen et al. 2007. These expanding atmospheres were shown to be sufficiently dense to produce the absorption in Lyα due to natural line broadening mechanism.However, the detection of absorption in the resonant lines of heavy elements such as OI, CII, and SiIII , Linsky et al. 2010, has shown that the absorbing material of planetary origin far beyond the Roche lobe has to be considered as well (Ben-Jaffel & Sona Hosseini 2010, Shaikhislamov et al. 2018a. The presence of a huge hydrogen corona also is a prerequisite for the explanation of strong in-transit Lyα absorption of GJ436b. By this, there is another crucial factor, besides of the Roche lobe effect, which has to be properly taken into account in the modeling of large-scale plasma dynamics around the close-orbit exoplanetsthe stellar wind (further SW) plasma. Self-consistent description of the escaping multi-co...